In this paper, we study the anomalous temperature dependence
of the anisotropic conductivity of
\(\alpha \) -(BEDT-TTF)\(_2\) I\(_3\)  using the TB model [1]}, [2]}, [3]}, [4]}
and acoustic phonons. Thus, the present paper is a natural extension of the previous study [5]}
in which a simplified model was used without the details of the lattice structure
of \(\alpha \) -(BEDT-TTF)\(_2\) I\(_3\) . By using the TB model,
we can automatically take into account the effects of tilting and anisotropy discussed at absolute zero  [6]}
to explore the temperature dependence.
It will be shown that the presence of acoustic phonons gives rise to conductivity being nearly constant at high temperatures.
We will also demonstrate
a crossover of the conductivity from a quantum regime at low temperatures
to a classical regime at high temperatures by focusing on a competition
between the tilted Dirac cone and the anisotropic velocity of the cone.
We use the TB model with transfer energies of  \(\alpha \) -(BEDT-TTF)\(_2\) I\(_3\) 
under pressure, which are well known compared with those of
other isostructural salts, BETS and STF.
Since the tilted Dirac cone is also obtained for BETS [7]}
and STF [8]},
it is expected that the present result
provides a common feature for these salts,
i.e., the nearly constant conductivity at high temperatures.
